(classic problem)
Definition: Find the weight (or length) of the shortest paths between all pairs of vertices in a weighted, directed graph.
See also Floyd-Warshall algorithm, Johnson's algorithm similar problems: single-source shortest-path problem, shortest path, minimum spanning tree, traveling salesman, all simple paths.
Note: The problem is to find the weights of the shortest paths between all pairs of vertices. For a map, it is to produce the (shortest) road distances between all cities, not which roads to take to get from one city to another.
After LK.
Author: PEB
If you have suggestions, corrections, or comments, please get in touch with Paul Black.
Entry modified 1 February 2005.
HTML page formatted Mon Feb 2 13:10:39 2015.
Cite this as:
Paul E. Black, "all pairs shortest path", in
Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 1 February 2005. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/allPairsShortestPath.html